Statistical machine learning methods for neuroscientific data: Analysing brain activity, psychopathology and cognitive function in adolescents

.title[
# Statistical machine learning methods for neuroscientific data: <br>Analysing brain activity, psychopathology and <br> cognitive function in adolescents<br><br>
]
.subtitle[
## Final Seminar<br>Owen Forbes<br>May 5 2023<br><br>
]
.author[
### 
]
.date[
### Distinguished Professor Kerrie Mengersen (Principal Supervisor)<br>Dr Paul Wu (Associate Supervisor)<br>Dr Edgar Santos Fernandez (Associate Supervisor)<br><br>Queensland University of Technology
]

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#### Mental Health in Adolescence

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#### Mental Health in Adolescence
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- Mental health issues are a significant and growing problem in youth populations (Sawyer et al., 2018; McGorry & Mei, 2018)]
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- Many mental health problems & disorders are thought to emerge in adolescence; period of rapid brain development and change (Paus et al., 2008; McGorry et al., 2011)]
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- Mental health risk in childhood & adolescence is understood to be **pluripotential**
  - Non-specific risk overlaps across a number of clinical diagnostic categories (Raballo & Poletti, 2020; Hartmann et al., 2019)]
--

👉 We need **improved data-driven statistical modeling** to better understand the <br> **complex relationships between neurophysiology and mental health in adolescence** 🧠

---
### Case-control and Data-driven Approaches

- Identifies differences between diagnosed and undiagnosed groups
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- Limited to find information within diagnostic categories based on clinical judgement
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- Limited generalisability / replicability outside of sample (Latzman & DeYoung, 2020)

- Identifies subgroups of symptoms or individuals based on patterns in data, rather than diagnostic categories / clinician judgement
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- Prioritises population-based cohort studies (Latzman & DeYoung, 2020)
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- Growing emphasis on data-driven electroencephalography (EEG) research to find new discoveries out of scope from traditional diagnostic categories (Loo et al., 2016; Keizer, 2019)

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### Electroencephalography (EEG) Data

- Records electrical brain activity <br> using electrodes on the scalp

- Signals represent cumulative activity <br> of rhythmic firing across networks <br> of many neurons <br>

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**Strengths**
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- High temporal resolution for measuring oscillations & dynamic brain states (Burle et al., 2015)

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- Low cost, widely available (Liedorp et al., 2009)

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- Non-invasive, low participant burden

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- Low signal-to-noise ratio (Wu et al., 2015)
  - Eye and muscle movements
  - Background electrical noise
  - Electrode contact quality
  
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- Non-stationary (Sun and Zhou, 2014)
  - Significant variation in underlying processes

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- High dimensionality 
  - Large number of channels & features

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#### Growing need for increased large scale research studies collecting data on brain, psychopathology and cognitive function

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**Longitudinal Adolescent Brain Study (LABS)**
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- Longitudinal cohort study of youth in the Sunshine Coast

- Follows participants from age 12 - 17

- Recruitment goal: 500 participants

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Thesis data scope:
- 59 individuals aged 12 years (T1)

- Resting state EEG, psychological distress, <br> sleep quality, cognitive function

- Chapters 3 & 4

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- Large cross-sectional study in New York region

- Participants aged 5-21

- Goal: Biobank of 10,000 participants

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Thesis data scope:

- 503 participants aged 9-15

- Pre-processed resting state EEG, <br> psychopathology and cognitive function

- Chapters 5 & 6

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# Aims & Objectives

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### Applied Motivation

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Develop novel statistical methods to identify data-driven EEG phenotypes in adolescents
]

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Investigate relationships of phenotypes to psychopathology and cognitive function, with potential applications in personalised healthcare, risk prediction and early intervention
]

---

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(1) Develop an end-to-end pipeline for EEG-based clusters in adolescents **(Ch 3)**
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(1a) Using LABS data, examine associations with health measures. **(Ch 3 & 6)**
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(2) Build Bayesian Model Averaging framework to combine clusters with probabilistic allocation & model-based uncertainty **(Ch 4)**
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(2a) Assess clinical & applied utility of BMA features with case study using LABS EEG clusters **(Ch 4 & 6)**
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(3) Develop nested functional analysis framework for time series data including functional characteristics in latent states **(Ch 5)**
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(3a) Investigate associations between functional analysis outputs & health measures using HBN data **(Ch 5 & 6)**
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(4) Replicate and compare feature extraction and clustering pipelines (1) and (3) across LABS and HBN data **(Ch 6)**
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(4a) Explore cross-method, cross-sample replication of robust EEG phenotypes in adolescents using methods in (1) and (3) **(Ch 6)**
]]

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# Chapter 3
# EEG-based clusters differentiate psychological distress, sleep quality and cognitive function in adolescents

---
### Chapter 3: Novel Contributions

- First work to investigate phenotypes using unsupervised clustering of EEG data from a population sample of adolescents

- New insights about the presence of resting state EEG phenotypes, and clear associations with psychological distress, sleep quality and cognitive function

- Novel statistical pipeline implemented in **freely available open source software** (R and MATLAB) for clinicians and researchers to apply in their own work

- SAGE Award for Best HDR Student Publication (Faculty of Science) 2022

- Published in _Biological Psychology_

---

### Chapter 3: Methods
<center>
<img src="data:image/png;base64,#imgs/P1Fig1.png" width="800" />
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<br>
- Time-averaged summary features selected _a priori_
.pull-right[
<img src="data:image/png;base64,#imgs/summary_features_diag.jpeg" width="350" />
]
--

- Dimension Reduction with PCA

- 3 clustering algorithms

- Overlapping 'core' clusters

---
##### Chapter 3: Results

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.pull-left[
<img src="data:image/png;base64,#imgs/c3_clusters_static.jpeg" width="300" />
<img src="data:image/png;base64,#imgs/P1Fig5_wide.png" width="350" />
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<img src="data:image/png;base64,#imgs/P1Fig7.png" width="450" />
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### Exciting preliminary results

- Clusters have distinct EEG characteristics and substantial differences in mental health and cognition

- Indicate resting state EEG phenotypes in adolescents, potential *risk* and *protective* biomarkers

--
.content-box-yellow[
Can we develop a better way to combine multiple clustering algorithms, incorporating model-based uncertainty? **(Chapter 4)**
]
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.content-box-green[
Can we use more sophisticated methods to characterise EEG, include temporal information, and avoid coarse canonical summary features? **(Chapter 5)**
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How robust are the phenotypes associated with these clusters? Do we find similar results using different samples, and different methods? **(Chapter 6)**
]

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class: middle, center 
# Chapter 4
# _clusterBMA_: Bayesian Model Averaging for Clustering

---

### Chapter 4: Novel Contributions

- First implementation of Bayesian model averaging to combine solutions across multiple clustering algorithms

- Offers unique features for ensemble clustering including **quantification of model-based uncertainty** and probabilistic allocation to combined clusters

- Substantially better accuracy in benchmarking performance compared to other ensemble algorithms, particularly for high-dimensional data with low separation between clusters

- Implemented in open source & freely available **R package** for data scientists & practitioners to apply across various fields

- Preprint has been cited

- Trending on DeepAI

- Used by researchers at UWA and US government agency

---

## Which clustering algorithm?

.pull-left[<iframe src="imgs/plot_3d_km.html" width="500" height="250" scrolling="yes" seamless="seamless" frameBorder="0"> </iframe>]

.pull-right[<iframe src="imgs/plot_3d_hc_colourfix.html" width="500" height="250" scrolling="yes" seamless="seamless" frameBorder="0"> </iframe>]

.pull-left[<iframe src="imgs/plot_3d_gmm.html" width="500" height="250" scrolling="yes" seamless="seamless" frameBorder="0"> </iframe>]

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## Inconsistent clustering across algorithms

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### Which clustering algorithm?

- Different algorithms will emphasise different aspects of clustering structure

- Choosing one 'best' model often arbitrary, unclear choice

- ➡️ **Inference not calibrated for model-based uncertainty**

- Locking into one method loses insights offered by other methods about plausible clustering structure

- simple
  
  - flexible

- intuitive 
]

---

### Combining Clustering Results with Bayesian Model Averaging

- Limited development for Clustering
  - Finite mixture models (Russell et al., 2015)
  - Naive Bayes classifiers (Santafe & Lozano, 2006)
  - Lacks implementation across multiple clustering algorithms

--
<br>

**Advantages**

- 🆒 Weighted averaging of results incorporating model quality / goodness of fit

- 💯 Intuitive framework for **probabilistic** inferences combining results from **different clustering algorithms**

- 😮 Each input solution can have a different number of clusters `$K$`

- 😎 **Quantify model-based uncertainty and enable more robust inferences** calibrated accordingly

---

### Bayesian Model Averaging: Basics

`$$P(\Delta | Y) = \sum_{l=1}^L (\Delta | Y, M_l)P(M_l|Y)$$`

--
<br>
<br>

`$$P(M_l|Y) = \frac{P(Y|M_l)P(M_l)}{\sum_{l=1}^L P(Y|M_l)P(M_l)}$$`

---

#### BMA for Mixture Models - BIC weighting
- `$P(Y|M_l)$` typically involves a difficult/intractable integral and is often approximated for many applications (Fragoso et al., 2018)

- **Russell et al. (2015)** weight results from multiple GMMs according to BIC

`$$P(M_l \lvert Y) \approx \frac{exp(\frac{1}{2}{BIC}_l )}{\sum_{l=1}^L { exp(\frac{1}{2} BIC_{l}) }}$$`

- BIC definition for GMM

`$${BIC}_l = 2\log(\mathcal{L}) - \kappa_m \log(N)$$`

- GMM likelihood

`$$\mathcal{L}(\Theta) = \sum_{n=1}^N \sum_{k=1}^K{\pi_k\mathcal{N}(x_n|\mu_k, \Sigma_k)}$$`
--

- Multivariate Gaussian density

`$$\mathcal{N}(x|\mu, \Sigma) = \frac{\exp\left\{ -\frac{1}{2} (y-\mu)^T \Sigma^{-1}(y-\mu)\right\}}{|\Sigma|^{\frac{1}{2}} (2 \pi)^{\frac{D}{2}}}$$`
                 
                 
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### Aside: Cluster internal validation indices

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- Often used as a proxy for model quality in clustering
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- Choose between candidate models with different numbers of clusters `$k$`

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- Interpreted similarly to marginal likelihood/model evidence

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- Typically measure compactness and/or separation of clusters

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Compared to BIC...
  - Agnostic to clustering algorithm
  - Typically do not require likelihood term

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### New proposed weighting / approximation for posterior model probability

BIC for GMM driven by **Multivariate Gaussian density:**

`$$\mathcal{N}(x|\mu, \Sigma) = \frac{\exp\left\{ -\frac{1}{2} (y-\mu)^T
                 \Sigma^{-1}(y-\mu)\right\}}{|\Sigma|^{\frac{1}{2}} (2 \pi)^{\frac{D}{2}}}$$`

**Calinski-Harabasz Index**
- Ratio of separation to compactness (maximise)
`$$CH = \frac{\sum_i{n_i d^2(c_i,c)/(NC-1)}}{\sum_i{\sum_{x \in C_i}d^2(x,c_i)/(n-NC)}}$$`

**S_Dbw Index**

- Sum of intra-cluster scattering and inter-cluster density (minimise)
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<img src="data:image/png;base64,#imgs/S_Dbw_short.jpeg" width="400" />
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- CH and S_Dbw indices are both well validated in the context of comparing model quality across different clustering algorithms

---

### New proposed weighting / approximation for posterior model probability

CH and S_Dbw indices
- conceptually and mathematically similar to BIC
- Unlike BIC, can be calculated + directly compared across different clustering algorithms

New proposed weight:

<br>

Approximate posterior model probability for weighted averaging:
`$$P(\mathcal{M}_m \lvert Y) \approx \frac{\hat{\mathcal{W}}_m \left(\frac{1}{M}\right)}{\sum_{m'=1}^M \hat{\mathcal{W}}_{m'} \left(\frac{1}{M}\right)} = \hat{\mathcal{W}}_m.$$`

---

### Consistent quantity `$\Delta$` - Similarity matrices

Previous work (Russell et al., 2015) has used pairwise similarity matrices as `$\Delta$` for each model

- To get similarity matrix, multiply allocation matrix by its transpose:

`$$S_m = A_m A_m^T$$`

- **invariant to number and labelling of clusters across solutions**

---

### Consensus matrix

`\begin{equation}
  C = {\sum_{m=1}^M\hat{\mathcal{W}}_m S_m}.
\end{equation}`

---

### Consensus matrix ➡️ Matrix factorisation ➡️ Cluster allocation probabilities

- Symmetric Simplex Matrix Factorisation (SSMF; Duan, 2020) to get `$N \times  K$` allocation matrix `$A_m$` from `$N \times N$` consensus matrix `$C$`

- Generates probabilistic cluster allocations from pairwise probabilities

- Includes L2 regularisation step to reduce overfitting & redundant clusters

---

## Case study: Clustering adolescents based on resting state EEG recordings

---

### Model results

---

### Model results ➡️ Similarity matrices

.pull-left[**k-means** `$\hat{\mathcal{W}}_m = 0.36$`
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<img src="data:image/png;base64,#imgs/km_similarity.png" width="300" />
]

.pull-right[**HC** `$\hat{\mathcal{W}}_m = 0.27$`
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<img src="data:image/png;base64,#imgs/hc_similarity.png" width="300" />
]

.pull-left[**GMM** `$\hat{\mathcal{W}}_m = 0.37$`
<br>
<img src="data:image/png;base64,#imgs/gmm_similarity.png" width="300" />
]

---

### Model results ➡️ Similarity matrices ➡️ Consensus matrix

---

### BMA Clusters with allocation uncertainty

.center[
<iframe src="imgs/eeg_3d_BMA_size_uncertainty_301122.html" width="750" height="400" scrolling="yes" seamless="seamless" frameBorder="0"> </iframe>
]

- **Uncertainty can be propagated forward for further analysis in a Bayesian framework**

---

### Benchmarking study: Feature comparison with other ensemble approaches

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### Benchmarking study: Accuracy comparison

- 9 clustering algorithms
- Simulated data with differing dimensions (2, 10, 50) and separation (high, medium, low)
- 10 simulated datasets for each combination of dimensions X separation

--
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<img src="data:image/png;base64,#imgs/benchmarking_results_table.jpeg" width="850" />
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---

## A quick demo

---

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# Chapter 5
# Functional analysis within latent states for neuroscientific data: Linking resting state brain activity, psychopathology and cognitive function in young people

---

### Chapter 5: Novel Contributions

- Novel nested framework for functional data analysis (FDA) of functional time series data

- Integrated analysis of functional latent states using FHMM, and functional characteristics within states using FPCA

- More nuanced insights into variation in resting state EEG, less reliant on flawed assumptions and canonical features

- In HBN data, Bayesian regression models show substantial assocations of temporal dynamics and functional characteristics within states, with measures of psychopathology and cognitive function

- Lays a foundation for more sophisticated phenotype identification including temporal and functional characteristics (Chapter 6)
--

- Implemented in open source & freely available software in R for practitioners to apply across various fields

--
.content-box-red[
**In preparation for submission to _Statistical Methods in Medical Research_**
]

---

### Functional analysis within latent states - Overview

---

---

<center>
<img src="data:image/png;base64,#imgs/beyonce_flawless.gif" width="600" />
</center>
---

#### Functional Data Analysis (FDA)

- Data represented as functions -- e.g. curves over a continuous functional domain like time or frequency

- Analyse influential characteristics across the whole functional domain of interest

- Copes well with high dimensionality of neuroscience data

Summary features selected _a priori_]

FDA - information across whole curve
]

---

#### Functional Hidden Markov Models

Objective Function

- Similar to regular HMM, but emission function is not a PDF --> function based on L2 distance measure between each curve and mean curve for each state (Martino 2020)

---

#### Functional Principal Component Analysis

.content-box-red[
Captures the essential patterns of variation in functional data in terms of scores on **eigenfunctions** (Ramsay et al., 2009)
]
--

FPCA expansion

--
<br>
Finite n. of functional principal components, `$C$`

---

### _flawless_  analysis - Overview
<center>
<img src="data:image/png;base64,#imgs/flawless_model_diagram_updated.png" width="600" />
</center>

---

### FHMM - Latent State Centroids

---
### Latent State 1 - Functional Principal Components

---

### FHMM - Latent State Occupancy

Most common combinations:
- State 1 only (25.6%)
- States 1 and 2 (21.5%)
- State 2 only (9.3%)
- States 3 and 4 (6.4%)
- State 3 only (6.0%)
- State 4 only (5.6%).
]

--
.pull-right[
<img src="data:image/png;base64,#imgs/histograms_wide.png" width="550" />

- Most visit 1 (n = 234; 46.5%) or 2 (n = 205; 40.8%) latent states

- A majority (n = 479; 95.2%) make between 0 and 4 transitions between states over the recording period.

]
---

- Rich & nuanced empirical insights: Functional latent states; Temporal dynamics; Functional variation within states

- Bayesian Regression models: Substantial associations between FHMM & FPCA-within-state outputs, psychopathology and cognitive function

.content-box-blue[**Relative to traditional methods**: 
Less information loss; Fewer flawed assumptions from canonical summary features; Broadens scope beyond traditional features of interest
]
--

.content-box-yellow[**Relative to either method alone**:
Avoids compressing over distinct latent states (vs. FPCA alone); Identifies functional variation within states (vs. FHMM alone)
]
--

.content-box-green[**Relative to multi-dimensional functional analyses for EEG**:
Integrated insights + relationships across multiple levels of analysis; Better interpretability at each level
]

---

class: middle, center 
# Chapter 6
# Data-driven phenotypes of resting state brain activity in adolescents: Cross-method, cross-sample replication and extension using functional analyses

---

#### Chapter 6: Novel Contributions

.content-box-blue[(1) **Cross-sample replication** of phenotypes from Chapter 3 clustering (Summary Features) across LABS and HBN datasets
]
--

.content-box-yellow[(2) **Cross-method replication** of phenotypes from Chapter 3 (Summary Features) and Chapter 5 (FHMM States) with HBN data
]

.content-box-green[(3) **Extension of phenotypes** by clustering _flawless_ analysis outputs for latent state dynamics and FPC scores with HBN data
]

- Consistent patterns of association with psychopathology and cognitive function

- Replication indicates more substantial evidence & lays foundation for clinical utility in the context of personalised healthcare and risk prediction

**In preparation for submission to _Nature Neuroscience_ **

---
#### (1) **Cross-sample replication** of Chapter 3 clustering across LABS and HBN datasets

---

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#### Health characteristics across Pipeline 1 clusters (time-averaged summary features)

---
#### (2) **Cross-method replication** of clustering from Chapter 3 (Summary Features) and Chapter 5 (FHMM States) with HBN data

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#### (3) **Extension of phenotypes** by clustering ( _flawless_ ) outputs for latent state dynamics and FPC scores with HBN data

---

.content-box-green[
🧠 ⭐ Cross-method, cross-sample replication of resting state EEG phenotypes in adolescents, and extension of more sophisticated phenotypes based on latent states, temporal dynamics, and functional characteristics within states
]

--
<br>

.content-box-purple[
🔥 🆒 😎 Strong foundation for potential clinical applications - risk/protective biomarkers, support early intervention and care planning personalised medicine 💯💯💯
]

---
# Limitations

.content-box-red[Cross-sectional data - limits understanding of phenotypes and health measures changing within individuals over time
]
--

.content-box-red[Single electrode data - limits understanding of spatial patterns of brain activity and functional connectivity
]

---
# Future Directions

.content-box-green[
- Longitudinal data & time-series analyses - understand longer term patterns of change and health risk

- Multi-electrode data - investigate spatial patterns & functional connectivity

- Combine EEG with other neuroimaging modalities (e.g. Diffusion Tensor Imaging, Functional MRI)
]

.content-box-blue[
- Development of user-friendly software with GUIs for testing in clinical settings
]

---

# Acknowledgements

* Supervisors: Kerrie Mengersen, Paul Wu and Edgar Santos-Fernandez

* Panel members: David Lovell, Kate Helmstedt

* PhD stipend and travel funding: Kerrie, QUT, CDS, ACEMS, SSA, IBS-AR

* Researchers, Participants & Caregivers for LABS and HBN studies

* Collaborators: Paul Schwenn, Hongbo Xie

* Friends, family, my partner Satomi

**_clusterBMA_  R package: bit.ly/clusterBMA**

- 🐦 Twitter: **@oforbes22**

---

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### References

Raballo, A. and Poletti, M. (2020). Advances in early identification of children and adolescents at risk for psychiatric illness. Current Opinion in Psychiatry, 33(6):611-617.

Ramsay, J. O., Hooker, G., & Graves, S. (2009). Functional data analysis with R and MATLAB: Springer Science & Business Media.

Tenke, C. E., & Kayser, J. (2005). Reference-free quantification of EEG spectra: combining current source density (CSD) and frequency principal components analysis (fPCA). Clinical Neurophysiology, 116(12), 2826-2846.
Chicago

Wu, W., Nagarajan, S., and Chen, Z. (2015). Bayesian Machine Learning: EEGMEG signal processing measurements. IEEE Signal Processing Magazine, 33(1):14-36.

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### FPCA & Bayesian Regression

- Bayesian regression models indicated substantial associations between:

* Latent state temporal characteristics

* **Functional frequency characteristics within states (FPCA scores)**

* Outcome: Health measures relating to psychopathology & cognitive function
]
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#### Answer to Conor's Question - Exciting Findings from Chapter 6 😎 (extended phenotypes)

.pull-left[
<img src="data:image/png;base64,#imgs/fingerprints_p3_pipeline_5only.png" width="450" />
]

- Clusters based on FHMM and FPCA outputs from all latent states

<img src="data:image/png;base64,#imgs/c5_table1.jpeg" width="450" />
]

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### FHMM Details

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### S_Dbw Details

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.pull-left[
#### *k*-means

- 'Hard' clustering
- Minimises within-cluster sums of squares]

.pull-right[**k-means objective function** <br>
`$$J = \sum_{i = 1}^K (\sum_k{\lvert \lvert x_k - c_i \rvert \rvert ^2})$$`]

- 'Hard' clustering
- Each observation starts out in its own cluster
- Repeated pairwise fusion of clusters that minimises change in within-cluster sums of squares (Ward)]

.pull-right[**Ward's objective function** <br>
`$$D(c_1,c_2) = \delta^2(c_1,c_2) = \frac{\lvert c_1 \rvert \lvert c_2 \rvert }{\lvert c_1 \rvert + \lvert c_2 \rvert} \lvert \lvert c_1 - c_2 \rvert \rvert ^2$$`]

.pull-left[
#### Gaussian Mixture Model
- 'Soft' clustering
- Models data as coming from a mixture of Gaussian distributions
- Restrictive distribution ('thin tails')
  - Tends to prioritise cluster compactness, may tend to 'overcluster']

.pull-right[**Mixture of multivariate Gaussians** <br>
`$$p(x_n|\mu, \Sigma, \pi,K) = \sum_{k=1}^K{\pi_k\mathcal{N}(x_n|\mu_k, \Sigma_k)}$$`]

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#### Chapter 3 details - Summary Features

**Features**

- Power in canonical bands -- Delta (0-4 Hz), ..., Beta (12-16 Hz)

- Total Power

- Individual Alpha Frequency

- Spectral Edge Frequency

- Spectral Entropy

**Principal Component Analysis**
- 3 PCs explained 80.6% of the variance

**Clustering**

- k-means

- Hierarchical Clustering

- Gaussian Mixture Model